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The purpose of this paper is to elaborate a robust model‐based protective control algorithm for multi‐mass motor drives that are subjected to physical and safety constraints on their variables.

The algorithm relies on the off‐line computed maximum robust controlled invariant set or its approximation for the given drive system and imposed constraints. It can be used to patch any existing drive control scheme with a firm constraints satisfaction guarantee. The online patch implementation is actually a simple correction of the control signal computed with the existing control scheme, with a mandatory state observer.

Performance of the patch is tested on a two‐mass drive system in combination with classical two‐mass drive speed controllers – P+I and reduced state controller. All constraints violations that exist in the presented responses obtained without the protection patch are suppressed by using the patch which shows the effectiveness of the approach. A brief implementation analysis shows that a digital signal processor could be used for online implementation of the controller with the protective patch.

Robust invariant sets theory is efficiently and effectively used in a new application area – protection of multi‐mass electrical drives.

Based on knowledge of the variables of a link system and their interrelation, the purpose of this paper is to show how it is possible to specify all the objects relating to dependency chains of a discrete system which are essential in systemic analysis of any system.

An algorithm is designed based on previously developed theoretical concepts which enables the discovery of the aforementioned objects.

A tool has been developed which is able to analyse any system with given variables and dependencies in a fast and economical manner.

These results can be applied to a number of cases. For example, in the case of an ecosystem, the structural function associated with each species of the ecosystem can be determined, it could be ascertained whether a group of species covered another group of species, whether there is an invariant group of species can be determined, and the orbit of each species analysed.

The algorithm presented in this paper is innovative in that it is a direct transfer of the theoretical results presented in recent publications, and therefore presupposes a different treatment of the qualitative analysis of the system.

The purpose of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on an algorithm and applying an interpretation of chaos theory developed in the context of General Systems Theory and Big Data.

Tourism is one of the most digitalized sectors of the economy, and social networks are an important source of data for information gathering. However, the high levels of redundant information on the Web and the appearance of contradictory opinions and facts produce undesirable effects that must be cross-checked against real data. This paper sets out the causal relationships associated with tourist flows to enable the formulation of appropriate strategies.

The results can be applied to numerous cases, for example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups, as well as analysing tourist behaviour in terms of the most relevant variables.

The technique presented here breaks with the usual treatment of the tourism topics. Unlike statistical analyses that merely provide information on current data, the authors use orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.

Measures are comparable if and only if measurement equivalence has been demonstrated. Although comparability and equivalence of measures are sometimes used interchangeably, we advocate a subtle but important difference in meaning. Comparability implies that measures from one group can be compared with measures from another group. It is a property of the measures, which is given or not. In particular, comparability presumes valid measures within each group compared. Measurement equivalence, by contrast, refers to the way measures are derived and estimated. It is intrinsically tied to the underlying theory of measurement. Thus, measurement equivalence cannot be dealt with in isolation. Its assessment has to be incorporated into the theoretical framework of measurement. Measurement equivalence is closely connected to construct validity for it refers to the way manifest indicators are related to the latent variable, within a particular culture and across different cultures. From this it follows that equivalence cannot, or should not, be treated as a separate issue but as a constitutive element of validity. A discussion of measurement equivalence without addressing validity would be incomplete.

The authors developed a lesson study innovation for bridging pre-service teachers' experiences in an early methods course and clinical experiences focusing on the development of technological pedagogical content knowledge (TPACK). The authors analyze one planning meeting by a lesson study team comprised of four pre-service teachers and one cooperating teacher. The purpose of this research was to determine the nature of documentation during the online planning meeting and how the cooperating teacher facilitated the documentation process.

The authors used Gueudet and Trouche's (2009) documentation framework to determine the way the lesson study team in our study used all the resources available to plan a lesson. They analyzed the video recordings of the meeting to examine the interplay between material, didactical and mathematical components during the discussions. The material components included the Teacher Desmos Activity Builder and the eTextbook. The didactical components included assessment, scaffolding, multiple representations and problem-solving activities. The mathematical components pertained to systems of linear equations and inequalities with two variables.

The authors’ findings show that the cooperating teacher performed an invariant set of actions for improving the research lesson and, also, gave recommendations about how to implement the lesson. In facilitating the planning discussions, the cooperating teacher made explicit the relationship between material, didactical and mathematical components. The authors’ work has implications for supporting the preparation of facilitators of online planning sessions during lesson study.

The authors did not have access to the planning meeting where the PSTs created the draft of the research lesson. In addition, they are reporting the observations of only one online meeting.

The authors’ work has implications for supporting the preparation of facilitators of online planning sessions during lesson study.

Stress computation in finite element materially non‐linear analysis is an important problem that has perhaps been receiving less attention than it deserves. Not only does it consume a significant share of total computer time, but also inaccuracies and ‘savings’ thereupon may well jeopardize the gains aimed at by sophisticating elsewhere the numerical strategy. A well established algorithm for stress computation is reviewed in detail, illustrating a number of computational hazards and proposing simple solutions.

This paper seeks to analyze ecological networks from a different viewpoint, using the concepts of orbits, coverage, invariant sets, etc.

A very simple view of ecosystems is presented, without delving into their multiple properties. Specifically, an ecosystem will be considered a system containing living and non‐living entities whose interrelationships include those of predator‐prey and competition. On interpreting that orbits are associated with ecosystems' direct and indirect paths, it is possible to present a much more conceptual design of ecological networks.

An ecosystem's two most important relationships, those of predator‐prey and competition, appear to be interconnected with the concepts of coverage, invariance and orbit, with multiple properties.

There are many interesting analyses of ecological networks' indirect effects that develop the quantitative and qualitative theory of ecological networks. What is new in this study is that it is the first dealing with orbits in the field of ecosystems.

Based on some of the results and definitions provided in the paper “system linkage: structural functions and hierarchies” and adding new definitions that are in keeping with the spirit of the same paper, new results have been obtained that explore the utility of the structural input‐output function.

Our approach is based principally on the application of graph theory to the study of relationships between variables using specific set theory concepts.

A result such as the fact that A covers B, for example, can be interpreted in terms of the latter set being formed of direct influences from elements in the former set in relation to one or more than one relationships. Analogously, the invariant set concept may be interpreted as the set maintaining its structure and status, remaining constant with respect to any possible relationships.

From a practical point of view, in the context of the study of networks within an ecosystem, authors (such as Patten et al. and Patten) have demonstrated that indirect effects between the variables of an ecosystem outweigh direct effects. This is the notion that the present authors have borne in mind in order to extend previous results to indirect influences from a discrete perspective.